Instead of using ERK methods in the Butcher form, Shu and Osher suggested another representation of ERK methods in order to design high-order time-discretization methods for problem (REF ) in [1]}. By using their idea we can see that certain ERK methods can be rewritten as a convex combination of forward Euler methods. This decomposition is a sufficient and necessary condition for the SSP property. For the relation between Shu-Osher and Butcher representations and for a complete introduction to the topic we recommend monograph [2]}. A brief summary of current theoretical results can be found in the recent review [3]}. In what follows we use the corresponding Butcher form of explicit SSP Runge–Kutta methods. Next, we highlight results of [3]} and [2]} which will be used in this paper.
